The sides of a triangle are 18 cm, 27 cm, 36 cm.Find the perimeter of a triangle like this one if its smallest side is 36 cm.

A triangle is three points that do not lie on one straight line, connected by segments. In this case, the points are called the vertices of the triangle, and the segments are called its sides.

Similar triangles are triangles in which the angles are respectively equal, and the sides of one are respectively proportional to the sides of the other triangle.

In order to find the length of the sides of a triangle ΔА1В1С1 similar to this one, you need to find the coefficient of similarity of these triangles. The similarity coefficient is the number k equal to the ratio of the similar sides of similar triangles:

k = A1B1 / AB = B1C1 / BC = A1C1 / AC.

Since the smallest side AB of the ΔABS triangle is 18 cm, then:

k = 36/18 = 2.

Let’s calculate the remaining unknown sides of the triangle ΔА1В1С1. To do this, we multiply the corresponding sides of a similar triangle ΔABS by the similarity coefficient:

B1C1 = 27 2 = 54 cm;

A1C1 = 36 2 = 72 cm.

The perimeter of a triangle is the sum of all its sides:

P1 = A1B1 + B1C1 + A1C1;

Р1 = 36 + 54 + 72 = 162 cm.

Answer: the perimeter of the triangle ΔА1В1С1 is 162 cm.